Question

Two rods of same length and cross sections are joined end to end. Their thermal conductivities are in the ratio $2:3$. If the free end of the first rod is at $0^o$C and free end of the second rod is at ${100}^o$C , the temperature at the junction of the two rods after attaining steady state is:

• A. ${33.33}^{o}C$
• B. ${40}^{o}C$
• C. ${50}^{o}C$
• D. ${60}^{o}C$

Answer 1

The correct option is D ${60}^{o}C$

From the Fourier's law we know that heat transfer through a plane wall is given as:

$Q=\frac{KA\Delta T}{l}$

Here length and area both are same for both the rod.

So, $Q=K_1\Delta T$

So, $Q_1=K_1(T_1-T)$

$Q_2=K_2(T-T_2)$

On equating both $Q_1$ and $Q_2$ we get

$K_1(T_1-T)=K_2(T-T_2)$

$\frac{K_1}{K_2}=\frac{T-T_2}{T_1-T}$

$\frac{2}{3}=\frac{T-100}{0-T}$

$T={60}^{0}C$